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- Title
Split Casimir operator for simple Lie algebras in the cube of ad-representation and Vogel parameters.
- Authors
Isaev, A. P.; Krivonos, S. O.; Provorov, A. A.
- Abstract
In this paper, we constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations a d and deduced a certain class of subrepresentations in a d ⊗ 3 . The projectors onto invariant subspaces for these subrepresentations were directly constructed from the characteristic identities for the 3-split Casimir operators. For all simple Lie algebras, universal expressions for the traces of higher powers of the 3-split Casimir operators were found and dimensions of the subrepresentations in a d ⊗ 3 were calculated. All our formulas are in agreement with the universal description of (irreducible) subrepresentations in a d ⊗ 3 for simple Lie algebras in terms of the Vogel parameters.
- Subjects
LIE algebras; REPRESENTATIONS of algebras; CUBES; GENERATING functions; INVARIANT subspaces
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2023, Vol 38, Issue 6/7, p1
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X23500379